As someone who used to play with these a lot in childhood, knob was the word I used.
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Nico BurnsOct 12 '12 at 20:50

knob or ball is a great description of the part in that photo, but be forewarned that similar train sets have squarish pieces that are definitely not balls. They might be squarish knobs, but are definitely connectors. see photo @ bargaintoystore.co.uk/…
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Michael PaulukonisOct 18 '12 at 17:58

This is known as a "ball joint". They're often seen in puppets, armatures, and other toys, as well as in the human body.

Edit: Just saw the updated question. tchrist's suggestion of knob works great, and in describing how it works, you can simply say it plugs in or connects another piece. Although I think there's nothing wrong with exposing a 3-year-old kid to "advanced" terminology like joint.

Pictured: a LEGO Bionicle Ball Joint

Edit #2: Jon Hanna made a good point in the comments below. Upon closer inspection, it may be more accurate to describe the track as using a "pivot joint" (#5 in the picture below). I mistakenly assumed that the ball would plug into the next section of track rather than lay in the cut out groove.

I won't be miffed if another answer is now accepted instead as I think they're both excellent alternatives!

It's not a ball-joint though, since it isn't used to allow rotation through different planes as a ball-joint does, but rather to hold the two pieces of track in a single place. It's hence a knob.
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Jon HannaOct 12 '12 at 13:39

@JonHanna I can't verify it, since I don't own the train track in question, but I would assume that if the tracks weren't laid on the ground that they would be able to swivel. Keep in mind a ball joint doesn't need a full range of motion to be called as such (e.g. human hips). Regardless, I had already upvoted the other answers, which I think are just as good (and said as much in my previous edit and comments), though I stand by my answer and appreciate your clarification. :)
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ZairjaOct 12 '12 at 14:04

2

The track doesn't move. It can do though if you lift it up, so it does act as a ball-joint in that condition, though it isn't used for it. In that case, it is a specific sort of ball-joint - an enarthrosis - which is to say a ball-and-socket joint where the socket covers more than half of the ball. I shall resist offering enarthrosis as my answer though, as cool a word as it is :)
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Jon HannaOct 12 '12 at 14:45

1

I wonder if "joint" is the right term. It doesn't fit the mechanics definition "a connection between two rigid bodies which allows movement with one or more degrees of freedom between them" (wikipedia). Not sure about this, interested in more discussion.
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David WOct 12 '12 at 17:06

It may go without saying, but I would add that all the answers provided for the OP should probably be used at least once. I'm pretty sure it's a good thing to promote a rich vocabulary, so long as the kid isn't overloaded. Some words may be beyond his ken (and pronunciation) at that age.
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ZairjaOct 12 '12 at 13:12

1

"Connector" is what we called it when I taught Sunday School. My students would get confused when I called it a "joint" because they either had a pre-existing mental association of that word with drugs, or because to them "joint" meant something like "elbow" -- that bends. (Should mention that I taught Sunday school in a not-so-nice part of town, hence the drug terminology known to 5 year olds.)
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Roddy of the Frozen PeasOct 12 '12 at 14:12

I agree with @Zairja: introduce both words. Generically it's a connector; specifically a knob connector that fits in the slot connector.
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ghoppeOct 12 '12 at 18:00